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Article in peer-reviewed journal

advanced nonlinear studies 7, 3 (2007) 491-511

Global existence for quadratic systems of reaction-diffusion

Laurent Desvillettes1, Klemens Fellner2, Michel Pierre3, Julien Vovelle3, 4

We prove global existence in time of weak solutions to a class of quadratic reaction-diffusion systems for which a Lyapounov structure of LlogL-entropy type holds. The approach relies on an a priori dimension-independent L-2-estimate, valid for a wider class of systems includingalso some classical Lotka-Volterra systems, and which provides an L-1-bound on the nonlinearities, at least for not too degenerate diffusions. In the more degenerate case, some global existence may be stated with the use of a weaker notion of renormalized solution with defect measure, arising in the theory of kinetic equations.

1:	CMLA - Centre de Mathématiques et de Leurs Applications
2:	Fakultät für Mathematik
3:	IRMAR - Institut de Recherche Mathématique de Rennes
4:	LATP - Laboratoire d'Analyse, Topologie, Probabilités

Keyword(s) : reaction-diffusion system – Lotka-Volterra systems – weak solutions – renormalized solutions – global existence – entropy methods

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http://hal.archives-ouvertes.fr/hal-00364787

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From: Maryse Collin <>

Submitted on: Friday, 27 February 2009 11:49:26

Updated on: Tuesday, 23 March 2010 11:35:49